Cosmology without cosmic variance

TL;DR

Combining large-scale galaxy redshift surveys with weak lensing data enables nearly sample-variance-free measurements of cosmic growth rates, significantly enhancing tests of gravity models at low redshift.

Contribution

This paper demonstrates that joint redshift and lensing surveys can measure the growth rate of structure without sample variance, surpassing traditional methods in constraining cosmological parameters.

Findings

Lensing and redshift data combination reduces uncertainty in growth rate measurements.

Sample variance can be effectively eliminated in the linear regime with combined surveys.

A survey of 10^6 redshifts can measure the growth exponent with high precision.

Abstract

We examine the improvements in constraints on the linear growth factor G and its derivative f=d ln G / dln a that are available from the combination of a large-scale galaxy redshift survey with a weak gravitational lensing survey of background sources. In the linear perturbation theory limit, the bias-modulation method of McDonald & Seljak allows one to distinguish the real-space galaxy clustering from the peculiar velocity signal in each Fourier mode. The ratio of lensing signal to galaxy clustering in transverse modes yields the bias factor b of each galaxy subset (as per Pen 2004), hence calibrating the conversion from galaxy real-space density to matter density in every mode. In combination these techniques permit measure of the growth rate f in each Fourier mode. This yields a measure of the growth rate free of sample variance, i.e. the uncertainty in f can be reduced without bound by increasing the number of redshifts within a finite volume. In practice, the gain from the absence of sample variance is bounded by the limited range of bias modulation among dark-matter halos. Nonetheless, the addition of background weak lensing data to a redshift survey increases information on G and f by an amount equivalent to a 10-fold increase in the volume of a standard redshift-space distortion measurement---if the lensing signal can be measured to sub-percent accuracy. This argues that a combined lensing and redshift survey over a common low-redshift volume is a more powerful test of general relativity than an isolated redshift survey over larger volume at high redshift. An example case is that a survey of ~10^6 redshifts over half the sky in the redshift range $z=0.5\pm 0.05$ can determine the growth exponent \gamma for the model $f=\Omega_m^\gamma$ to an accuracy of $\pm 0.015$, using only modes with k<0.1h/Mpc, but only if a weak lensing survey is conducted in concert. [Abridged]